包含方程x(ω)∈F(ω,x(ω),y(ω)),y(ω)∈G(ω,x(ω),y(ω))随机解的存在性

Existence of Random Solutions to the Inclusion Equations x(ω)∈F(ω,x(ω),y(ω)), y(ω) ∈G(ω,x(ω),y(ω))

在满足Opial条件的可分Banach空间内证明了包含方程x(ω)∈F(ω,x(ω),y(ω)),y(ω)∈G(ω，x(ω)，y（ω))随机解的存在性．

Int E be a weakly compact convex subset of a separable Banach space satisfying Opial's condition.Ω, ) a measurable space. Det F and C:Ω×E× E→CK(E) be mappings such that for each f∈C(E), ω ∈Ω, x ∈E, F(ω, x,f(x)) and C(ω, x,f(x)) are continuous random operators and F(ω, x, ) is K(ω) -Lipschitz and moreover H(C(ω,,x,y1, ), C(ω,x,y,2) ≤ ||y1 - y2||for any ω∈Ω ，x,y1,y2 ∈E. Then there etist measurable mappings u and v: Ω→E such that u(ω) ∈F(ω, u(ω), v(ω) ) and v(ω) ∈C(ω,u (ω), v (ω) ).